Seismic Fragility Quantitative Algorithm Based on Monte Carlo Sampling and Max-min Method

Fragility quantitative algorithm is an important part of seismic PSA (probabilistic safety analysis). However, there is no algorithm for combining seismic fragility of multiple components. A new seismic fragility quantitative algorithm was explored and studied, which is based on Monte Carlo (MC) sampling and the maxmin method to calculate the fragility of basic event, minimum cutset (MCS), and minimum cutset combination. MC method is a random sampling technique, which is widely used in the field of nuclear physics. The basic idea of MC method is when the solution of the problem is the probability of an event, the frequency of the event can be obtained by experimental method, and the solution of the problem can be obtained. Seismic fragility refers to the conditional failure probability of equipment or structures given ground motion parameters (such as peak ground acceleration or peak spectral acceleration). Given the equipment failure mode and distribution parameters, a conditional failure probability curve can be obtained, which shows the change with the ground peak acceleration. Seismic PSA usually assumes that the fragility of equipment and structures obeys double logarithmic normal distribution. Due to the particularity of seismic PSA quantification, the following three types of minimum cutset need to be considered. 1) Pure earthquake failure minimum cutset: The failure mode of all basic events are caused by earthquake, and without any logic success event. 2) Minimum cutset containing negate event: The failure mode of all basic events are caused by earthquake, and at least one basic event is logic success event. 3) Mixed cutset of earthquake failure and random failure: The basic events include earthquake failure events and random failure events. For accident sequences involving seismic and random failure mixed cutset, and negated event minimum cutset, the minimal cutsets upper bound (MCUB) method is used to quantify the sequence. The results of the Monte Carlo sampling and the maxmin method are consistent with the theoretical values and a new feasible algorithm for the seismic fragility quantification in engineering applications is provided. When the method introduced is used to calculate the fragility of the accident sequence only including earthquake failure, it is not necessary to use MCUB or other cutset quantification algorithms, and the seismic capacity of the accident sequence can be obtained only by comparing the seismic capacity of the basic event and the minimum cutset and then the fragility curve of the accident sequence can be obtained, and the calculation result is of high accuracy. The fragility algorithm introduced is especially suitable for the situation when pretree modeling is used, the earthquake damage state accident sequence usually only includes earthquake failure.